TSTP Solution File: ITP390_1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:30:47 EDT 2024

% Result   : Theorem 62.79s 8.65s
% Output   : CNFRefutation 62.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (  15 unt;   0 typ;   0 def)
%            Number of atoms       :  188 (  21 equ)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :   35 (  16   ~;  12   |;   4   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  143 ( 143 fml;   0 var)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   24 (  22 usr;  12 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   45 (   0 sgn  27   !;  12   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f10,axiom,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( 'fun_app$k'('uu$',X0)
    <=> ? [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).

tff(f100,conjecture,
    'fun_app$s'('f$','x$') = 'fun_app$s'('g$','x$'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture99) ).

tff(f101,negated_conjecture,
    ( ~ 'fun_app$s'('f$','x$') = 'fun_app$s'('g$','x$') ),
    inference(negated_conjecture,[],[f100]) ).

tff(f102,axiom,
    'member$a'('x$','collect$'('uu$')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis100) ).

tff(f103,axiom,
    ! [X0: 'A_ell2_a_ell2_cblinfun$',X1: 'B_ell2_b_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) = 'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).

tff(f262,axiom,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
      ( 'member$a'(X0,'collect$'(X1))
    <=> 'fun_app$k'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).

tff(f857,plain,
    'fun_app$s'('f$','x$') != 'fun_app$s'('g$','x$'),
    inference(flattening,[],[f101]) ).

tff(f1544,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( ( 'fun_app$k'('uu$',X0)
        | ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
      & ( ? [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) = X0 )
        | ~ 'fun_app$k'('uu$',X0) ) ),
    inference(nnf_transformation,[],[f10]) ).

tff(f1545,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( ( 'fun_app$k'('uu$',X0)
        | ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
      & ( ? [X4: 'A_ell2_a_ell2_cblinfun$',X5: 'B_ell2_b_ell2_cblinfun$',X6: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X4),X5)),X6) = X0 )
        | ~ 'fun_app$k'('uu$',X0) ) ),
    inference(rectify,[],[f1544]) ).

tff(f1546,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( ? [X4: 'A_ell2_a_ell2_cblinfun$',X5: 'B_ell2_b_ell2_cblinfun$',X6: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X4),X5)),X6) = X0 )
     => ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1547,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( ( 'fun_app$k'('uu$',X0)
        | ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
      & ( ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 )
        | ~ 'fun_app$k'('uu$',X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f1545,f1546]) ).

tff(f1697,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
      ( ( 'member$a'(X0,'collect$'(X1))
        | ~ 'fun_app$k'(X1,X0) )
      & ( 'fun_app$k'(X1,X0)
        | ~ 'member$a'(X0,'collect$'(X1)) ) ),
    inference(nnf_transformation,[],[f262]) ).

tff(f2190,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
      ( ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 )
      | ~ 'fun_app$k'('uu$',X0) ),
    inference(cnf_transformation,[],[f1547]) ).

tff(f2361,plain,
    'fun_app$s'('f$','x$') != 'fun_app$s'('g$','x$'),
    inference(cnf_transformation,[],[f857]) ).

tff(f2362,plain,
    'member$a'('x$','collect$'('uu$')),
    inference(cnf_transformation,[],[f102]) ).

tff(f2363,plain,
    ! [X2: 'C_ell2_c_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun$',X1: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) = 'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f103]) ).

tff(f2474,plain,
    ! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
      ( 'fun_app$k'(X1,X0)
      | ~ 'member$a'(X0,'collect$'(X1)) ),
    inference(cnf_transformation,[],[f1697]) ).

cnf(c_76,plain,
    ( ~ 'fun_app$k'('uu$',X0_51)
    | 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0_51)),sK18(X0_51))),sK19(X0_51)) = X0_51 ),
    inference(cnf_transformation,[],[f2190]) ).

cnf(c_246,negated_conjecture,
    'fun_app$s'('g$','x$') != 'fun_app$s'('f$','x$'),
    inference(cnf_transformation,[],[f2361]) ).

cnf(c_247,negated_conjecture,
    'member$a'('x$','collect$'('uu$')),
    inference(cnf_transformation,[],[f2362]) ).

cnf(c_248,negated_conjecture,
    'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0_15),X0_27)),X0_52)) = 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0_15),X0_27)),X0_52)),
    inference(cnf_transformation,[],[f2363]) ).

cnf(c_355,plain,
    ( ~ 'member$a'(X0_51,'collect$'(X0_113))
    | 'fun_app$k'(X0_113,X0_51) ),
    inference(cnf_transformation,[],[f2474]) ).

cnf(c_43448,plain,
    'fun_app$k'('uu$','x$'),
    inference(superposition,[status(thm)],[c_247,c_355]) ).

cnf(c_45174,plain,
    'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17('x$')),sK18('x$'))),sK19('x$')) = 'x$',
    inference(superposition,[status(thm)],[c_43448,c_76]) ).

cnf(c_49373,plain,
    'fun_app$s'('g$','x$') = 'fun_app$s'('f$','x$'),
    inference(superposition,[status(thm)],[c_45174,c_248]) ).

cnf(c_60682,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_49373,c_246]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n031.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 22:28:16 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.44  Running TFA theorem proving
% 0.17/0.44  Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 62.79/8.65  % SZS status Started for theBenchmark.p
% 62.79/8.65  % SZS status Theorem for theBenchmark.p
% 62.79/8.65  
% 62.79/8.65  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 62.79/8.65  
% 62.79/8.65  ------  iProver source info
% 62.79/8.65  
% 62.79/8.65  git: date: 2024-05-02 19:28:25 +0000
% 62.79/8.65  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 62.79/8.65  git: non_committed_changes: false
% 62.79/8.65  
% 62.79/8.65  ------ Parsing...
% 62.79/8.65  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 62.79/8.65  
% 62.79/8.65  ------ Preprocessing... sf_s  rm: 146 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e  sf_s  rm: 83 0s  sf_e  pe_s  pe_e 
% 62.79/8.65  
% 62.79/8.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 62.79/8.65  
% 62.79/8.65  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 62.79/8.65  ------ Proving...
% 62.79/8.65  ------ Problem Properties 
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  clauses                                 731
% 62.79/8.65  conjectures                             175
% 62.79/8.65  EPR                                     58
% 62.79/8.65  Horn                                    529
% 62.79/8.65  unary                                   131
% 62.79/8.65  binary                                  280
% 62.79/8.65  lits                                    1821
% 62.79/8.65  lits eq                                 268
% 62.79/8.65  fd_pure                                 1
% 62.79/8.65  fd_pseudo                               0
% 62.79/8.65  fd_cond                                 18
% 62.79/8.65  fd_pseudo_cond                          28
% 62.79/8.65  AC symbols                              1
% 62.79/8.65  
% 62.79/8.65  ------ Input Options Time Limit: Unbounded
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  ------ 
% 62.79/8.65  Current options:
% 62.79/8.65  ------ 
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  ------ Proving...
% 62.79/8.65  
% 62.79/8.65  
% 62.79/8.65  % SZS status Theorem for theBenchmark.p
% 62.79/8.65  
% 62.79/8.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.79/8.65  
% 62.79/8.65  
%------------------------------------------------------------------------------